A Characterization of Linear Difference Equations Which are Solvable by Elementary Operations.
A Concept of Bernoulli Numbers in Algebraic Function Fields (II).
A conjecture in the arithmetic theory of differential equations
A generalization of the method of global relation.
A generalization of the sizes of differential equations and its applications to -function theory
A note on a connection between the Poincaré-Arnold-Melnikov integral and the Picard-Vessiot theory
We obtain an algebraic interpretation by means of the Picard-Vessiot theory of a result by Ziglin about the self-intersection of complex separatrices of time-periodically perturbed one-degree of freedom complex analytical Hamiltonian systems.
A note on a theorem of C. L. Siegel concerning Bessel's equation
A note on characterizations of rings of constants with respect to derivations
Let A be a commutative algebra without zero divisors over a field k. If A is finitely generated over k, then there exist well known characterizations of all k-subalgebras of A which are rings of constants with respect to k-derivations of A. We show that these characterizations are not valid in the case when the algebra A is not finitely generated over k.
A note on differentially algebraic solutions of first order linear difference equations.
A note on Frobenius divided modules in mixed characteristics
If is a smooth scheme over a perfect field of characteristic , and if is the sheaf of differential operators on [7], it is well known that giving an action of on an -module is equivalent to giving an infinite sequence of -modules descending via the iterates of the Frobenius endomorphism of [5]. We show that this result can be generalized to any infinitesimal deformation of a smooth morphism in characteristic , endowed with Frobenius liftings. We also show that it extends to adic...
A note on functional equations of the -adic polylogarithms
A partial factorization of the powersum formula.
A simple axiomatics for differentiation.
A structure theorem for differential algebras
Algebraic independence of elementary functions and its application to Masser's vanishing theorem.
Algèbres d'opérateurs différentiels et quotients des algèbres enveloppantes
An algebraic framework for linear identification
A closed loop parametrical identification procedure for continuous-time constant linear systems is introduced. This approach which exhibits good robustness properties with respect to a large variety of additive perturbations is based on the following mathematical tools: (1) module theory; (2) differential algebra; (3) operational calculus. Several concrete case-studies with computer simulations demonstrate the efficiency of our on-line identification scheme.
An algebraic framework for linear identification
A closed loop parametrical identification procedure for continuous-time constant linear systems is introduced. This approach which exhibits good robustness properties with respect to a large variety of additive perturbations is based on the following mathematical tools: (1) module theory; (2) differential algebra; (3) operational calculus. Several concrete case-studies with computer simulations demonstrate the efficiency of our on-line identification scheme.
An application of newton iteration procedure to -adic differential equations
An example of an arithmetic Fuchsian group.